When one asks questions about size, shape, or position, one is asking a question that requires knowledge in geometry to answer. Geometric knowledge can often be used to clarify relationships and can make abstractions more easily understood. As students learn and develop geometric ideas, their knowledge progresses through a hierarchy of levels, from the simple to the more complex. To assist students in learning to recognize shapes and how to analyze relevant geometric properties of such shapes and the relationships between such shapes, several prior art tools are often employed. For example, a student exploring the field of geometry may be asked to use tools such as a compass, a protractor, ruler, and ready made forms for shapes such as triangles, circles, squares.
While such tools work well for their intended purposes, one drawback with such tools is that the student must transport and keep track of a multiple piece geometry kit. Additionally, using “ready made” forms to make shapes (e.g. triangles, squares, etc.) detracts from the learning process. For example, when a student uses a form to make a triangle, relatively little knowledge as to how a right triangle is formed is required (like tracing a picture instead of drawing a picture). What is needed to address such drawbacks is a single tool that can perform most or all of the functions performed by a compass, a protractor, a ruler, and ready made forms while requiring the student to more fully understand how a geometric shape is formed.
Of a more practical nature, adequate knowledge of geometric relationships provides one with insights that are useful in everyday situations. Knowledge of geometry is helpful in the sciences, the arts, and in performing practical tasks, such as construction tasks. Eventually, students leave academia and start their careers and purchase homes. Many such former students, while not professional contractors, will often find it rewarding to undertake home projects. Such former students will maintain a tool box comprising wrenches, sockets, and screw drivers, and while one might find a square and tape measure, what will be sadly lacking in most tool boxes are geometric tools. What is needed is a single piece geometric device for performing a variety of geometric functions that students learn to use while in academia and continue to find useful later in life. Ideally, one embodiment of such a tool would be configured to fit within a typical tool box.
Additionally, such a geometric device should be equally useful to the professional contractor to solve geometric problems. For example, geometric problems are often encountered when performing tasks associated with plumbing a house. Consider the problem where a plumbing pipe emerges from a hole in the ceiling and must extend downwardly therefrom through a space (the height of the room) and then pass through a corresponding hole in the floor beneath. It is desirable that the hole in the floor be the same size as the hole in the ceiling and directly beneath it. In the past this has generally been attempted by measuring the distance from adjacent walls. This is very imprecise because walls rarely plumb true and the multiple measurements inevitably result in some degree of error. So the hole in the floor ends up being considerably larger than the hole in the ceiling, and having undesirably large gaps between the hole and the pipe it is intended to accommodate.
The same problem arises, when a pipe emerges horizontally from a hole in one wall and must extend through a space (the length of the room) to pass through a corresponding hole in an adjacent wall.
What is needed is a precision geometric device for performing a variety of geometric functions offering nearly endless options for exploring the intricacies of the world of geometry while providing a practical tool for addressing geometric problems such as projecting the center of a hole to a distant surface.